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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Sat Aug 04, 2007 3:56 am Post subject: |
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There is a logic involving that potential UR and the 79 pair in Box 9, but it eliminates the <3> from R1C9. R1C9 must match R9C8 to avoid the URs. This elimination does not solve the puzzle, however. |
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George Woods
Joined: 28 Mar 2006 Posts: 304 Location: Dorset UK
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Posted: Sat Aug 04, 2007 5:02 pm Post subject: My shameless solution |
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Marty R. wrote: | Quote: | The 379s in Boxes 3 and 9 might easily bea DR either by removing either 3 7 or 9 from all.
So for badness postulate that r9c8 is 7 - it is not difficult to see that this makes r1c5 7 and we have the dreaded DR in 39 So r9c8 must be 9 and hence a solution |
George, I can't follow the line of logic. If r9c8=7, then r9c5=8. The resulting 37 pair in box 2 forces r1c5=9.
Code: | 2 8 1 | 5 379 4 | 6 379 379
5 7 3 | 29 129 6 | 8 4 19
6 4 9 | 37 378 18| 5 2 137
----------------------------
7 13 6 | 8 123 12| 9 5 4
19 5 8 | 4 19 7 | 3 6 2
4 39 2 | 39 6 5 | 7 1 8
----------------------------
89 6 5 | 27 4 28| 1 379 379
3 2 7 | 1 5 9 | 4 8 6
189 19 4 | 6 78 3 | 2 79 5 |
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Code: |
+-------+----------+-----------+
| 2 8 1 | 5 37 4 | 6 379 379 |
| 5 7 3 | 29 29 6 | 8 4 1 |
| 6 4 9 | 37 . . | 5 2 . |
+-------+----------+-----------+
| 7 . 6 | 8 . . | 9 5 4 |
| . 5 8 | 4 . 7 | 3 6 2 |
| 4 . 2 | 39 6 5 | 7 1 8 |
+-------+----------+-----------+
| . 6 5 | 27 4 28 | 1 379 379 |
| 3 2 7 | 1 5 9 | 4 8 6 |
| . . 4 | 6 78 3 | 2 79 5 |
+-------+----------+-----------+
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Play this puzzle online at the Daily Sudoku site
I reached a different "crunch point" from yours ( and I didn't have the 9 in r1c9 But on my grid my logic seems to work!!! |
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Marty R.
Joined: 12 Feb 2006 Posts: 5770 Location: Rochester, NY, USA
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Posted: Sat Aug 04, 2007 5:16 pm Post subject: |
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Quote: | I reached a different "crunch point" from yours ( and I didn't have the 9 in r1c9 But on my grid my logic seems to work!!! |
I just copied the grid that was posted, which I thought you were working from. |
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George Woods
Joined: 28 Mar 2006 Posts: 304 Location: Dorset UK
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Posted: Sat Aug 04, 2007 5:59 pm Post subject: Final comment on shameful solution |
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On repeating the puzzle to get to my quoted crunch point I had trouble justifying the 1 in r2c9 and guess what ! the W Wing actin on 19 in Boxes 3 and 5 denies a 1 to r2c5.
The 9 at r9c8 (resulting from removal of 7 since it would give an UR) solves the puzzle in very quick time! |
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shoeless
Joined: 03 Aug 2007 Posts: 13
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Posted: Sun Aug 05, 2007 3:54 am Post subject: |
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Steve R wrote: | Welcome shoeless!
You can eliminate 2 from r4c5 using the xy-wing pivoted on (19) in r5c5 with pincers r2c5 and r4c6.
Steve |
Thanks Steve, that's what I needed. Amazing how obvious it is when someone points it out.
And thanks to you too Nataraj, for taking the time to explain the chain to me. After I studied that a bit, it made sense.
Regarding the 2 in r4c6, that is the next logical step when using the XY wing that Steve pointed out. |
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cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada
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Posted: Sun Aug 05, 2007 8:50 pm Post subject: |
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Quote: | ... and guess what ! ...the W Wing acting on 19 in Boxes 3 and 5 denies a 1 to r2c5. |
This is where I get lost with a lot of posts. Mr. Asellus directed me to a most excellent Suduko site which explained "Swordfish" - and showed that an earlier Swordfish solution was not valid. I thank him for that.
However, I did not see any references on that site to W wings. The only explanation of W wings I have found (on this site) implied that W wing solutions have to be contained within 3 linear blocks. So I can't, for the life of me see the right-angled triangle W wing referenced above.
.... And if we sort this out -- let's get into the claims for those URs, which I swear aren't there. |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Sun Aug 05, 2007 10:18 pm Post subject: |
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cgordon,
The "W-Wing" name was coined on this discussion board. I could search for the original threads and post links, but other than being interesting, it would take you a while to wade through them and figure it all out. So, I'll try to explain...
A W-Wing is a remote pair of bivalue cells, XY. Remote means that they are not "buddies." To form a W-Wing, there must be some sort of strong link on X the opposing ends of which these two cells separately "see". (The possibilities for this "external strong link" can get somewhat exotic and hard to see. The more you learn to see strong links, the easier they become to spot.)
The external strong link on X creates a weak link on Y between the two bivalue cells. This weak link allows elimination of Y from all "buddies" of the two bivalue cells.
In the current case...
Code: | +----------+-------------+-------------+
| 2 8 1 | 5 379r 4 | 6 379g 379g |
| 5 7 3 | 29 -129 6 | 8 4 w19 |
| 6 4 9 | 37 378 18 | 5 2 137 |
+----------+-------------+-------------+
| 7 13 6 | 8 123 12 | 9 5 4 |
| 19 5 8 | 4 w19 7 | 3 6 2 |
| 4 39 2 | 39 6 5 | 7 1 8 |
+----------+-------------+-------------+
| 89 6 5 | 27 4 28 | 1 379 379 |
| 3 2 7 | 1 5 9 | 4 8 6 |
| 189 19 4 | 6 78 3 | 2 79 5 |
+----------+-------------+-------------+ |
The W-Wing 19 bivalues are marked w. The external strong link is on <9> in R1: <9> is either in C5 or it is in Box 3. I have used r (red) and g (green) to mark the polarity of this link. R5C5 sees the <9> in R1C5 and R2C9 sees the <9>s in Box 3 R1. This means that one or both of our w cells must be <1>, which is a "weak link" on <1>. Any cells that can see both of these cells ("buddies") cannot contain <1>.
In this case, there is just one elimination, in R2C5, as marked. |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Sun Aug 05, 2007 11:01 pm Post subject: |
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cgordon,
I went back and reviewed the thread re: URs. But first...
I should mention that the name W-Wing was bestowed because George Woods first posted the related observation on this board. So, it's the "Woods-Wing," it seems. Subsequent research turned up earlier descriptions elsewhere of the general technique. Be that as it may, we seem to like this name hereabouts.
Also, there is no need for the W-Wing constituents to involve three colinear boxes. The early examples noted and discussed were of this form, but that was coincidental.
On this thread, George's first UR claim didn't make sense based on the puzzle grid that had been posted earlier (as Marty pointed out). It turns out, however, that if you first apply the <1> elimination from that W-Wing and do the simplifications, <7> is removed from R3C5. After that, George's argument holds and requires R9C8 to be <9> to avoid the UR.
I added a brief post (based upon the earlier grid) that the 79 in R9C8 eliminated <3> from R1C9 using UR logic. Perhaps you see this already. If not, refer to the grid in my previous post showing the W-Wing.
R9C8 must be <7> or <9>. If it is <7>, then three corners of R17C89 become 39 and only a <7> in R1C9 prevents the UR. The case of <9> is exactly analogous. So, R1C9 cannot be <3>. But, as I said, it wasn't a very helpful elimination. |
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cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada
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Posted: Mon Aug 06, 2007 1:59 pm Post subject: |
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Asellus:
I followed the logic of your W-wing solution. However, my understanding of W wings come from a graphic explanation for a colinear example given by Texcat (posted June 6) and a Type 2 example from jLo (July 4). Both relate to remote bivalue cells – but the links seems to be based on the NON APPEARANCE of each of the values in definable patterns. Your solution seemed to be based on good logic (it looked to me like a chain) but I didn’t see it related to any definitive rules that could be called a W Wing pattern or procedure. Of course I could be wrong ! |
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Marty R.
Joined: 12 Feb 2006 Posts: 5770 Location: Rochester, NY, USA
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Posted: Mon Aug 06, 2007 3:58 pm Post subject: |
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Craig,
I haven't followed this thread in excruciating detail, but I'd just like to throw out the following: Asellus's logic about the 9s in r1 is excellent, something I never would have noticed or figured out.
Alternatively, there is a strong link on 9s in column 4, each of which sees one of the "w" cells, which means one or the other of the "w" cells must be =1. I believe this is the essence of the W-Wing in its simplest, most basic form. |
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cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada
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Posted: Mon Aug 06, 2007 4:17 pm Post subject: |
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Marty: I agree Asellus's logic was very clever and perceptive - but could the same result have been derived from any system or technique - like something similar to the previously posted W wing techniques I mentioned. That's the only way I'm gonna find these solutions. |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Mon Aug 06, 2007 8:48 pm Post subject: |
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Marty,
Thanks! I saw the R1 link first. But, any external strong link serves the purpose.
cgordon,
Here is TexCat's June 6 graphic:
Code: | . . . | NotG NotG NotG | . . .
GW . . | . . . |NotW NotW NotW
NotW NotW NotW| . . . | . . GW
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I believe that what may help you out is to see that the "NotG" in the middle Box of the top row implies a strong link on G between the middle and bottom rows of that middle Box and that provides the "external strong link" for the W-Wing:
Code: | . . . | NotG NotG NotG | . . .
GgW . . | Gr Gr Gr |NotW NotW NotW
NotW NotW NotW| Gg Gg Gg | . . GrW |
At least one Gr and at least one Gg must be present in the middle and bottom rows of the middle Box if there is no G in the top row because the box must have a G and its position hasn't yet been determined (or the W-Wing would vanish!).
Here is the section of the puzzle from earlier in the same thread on which this was based. I've used r and g (red and green) again to show the strong links for the 78 W-Wing:
Code: | +------------+-------------+---------------+
| 24 38 5 | 468 346 9 | 246 7 1 |
| 247 13 6 | 78g 13 5 | 249 48r 28r9 |
| 147 9 78r | 1678 2 48 | 2456 3 68g |
+------------+-------------+---------------+ |
I hope that helps settle the confusion. I find that the "NotG" approach is not so useful in general except as a quick and easy way to check in simple W-Wing cases.
Yes, W-Wings are implication chains. But that is unremarkable: all the solving techniques of which I am aware can be expressed as chains, including UR techniques. The general chain form of the W-Wing, using Eureka notation, is:
(Y)Targets - (Y=X)W1 - (X)EL1 [...] = (X)EL2 - (X=Y)W2 - (Y)Targets
where W1 and W2 are the two W-Wing cells and EL1 and EL2 are the two ends of the External (Strong) Link. The ellipsis indicates that there can be any intervening chain. (On another thread, there were W-Wing examples involving finned fish and ER relationships for forming the external link!) |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Mon Aug 06, 2007 9:10 pm Post subject: |
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cgordon,
It took me a moment to find it, but here is jLo's graphic to which you referred:
Code: | +---------+---------+---------+ Type 2
| ~W |GW | |
|~g ~g | | | if GW and (~g or ~G) then ~W
|~g ~g | | |
+---------+---------+---------+
| | | |
| | | |
| | | |
+---------+---------+---------+
| GW |~W | |
| | ~G ~G | |
| | ~G ~G | |
+---------+---------+---------+
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I'm going to rewrite it a bit:
Code: | +--------+-------------+
| . . -W | GW . . |
| . . . | . . . |
| . . . | . . . |
+--------+-------------+
| . . . | . . . |
| . . . | . . . |
| . . . | . . . |
+--------+-------------+
| . . GW |-W . . |
| . . . | . NotG NotG |
| . . . | . NotG NotG |
+--------+-------------+ |
(The "-W"s indicate the potential eliminations.)
What we have here is an Empty Rectangle (ER) providing the external strong link for the W-Wing. All ERs work by having a strong link between the cells outside the ER. Here is how it looks:
Code: | +---------+---------------+
| . . . | GrW . . |
| . . . | . . . |
| . . . | . . . |
+---------+---------------+
| . . . | . . . |
| . . . | . . . |
| . . . | . . . |
+---------+---------------+
| . . GgW | Grg Gr Gr |
| . . . | Gg NotG NotG |
| . . . | Gg NotG NotG |
+---------+---------------+ |
I hope these examples have helped to clarify that the "non appearances" you mention are just alternate ways of indicating the presence of an external strong link, which is what is essential.
Note: I'm not a big fan of lists of "Types". So, I look for the fundamental underlying principles to see if there is a basic universal pattern. |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Mon Aug 06, 2007 9:40 pm Post subject: |
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I should give credit where due....
Reviewing the former threads reminds me that it was Keith, in a post on the "2 July VH" thread, who pointed out the essential nature of the external strong links in W-Wings and first made this clear to me. |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Mon Aug 06, 2007 9:52 pm Post subject: |
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I realized I should post a clarifying technical caveat:
The coloring I used in the previous posts regarding W-Wings is not conventional coloring and shouldn't be misunderstood as such. The links between the W-Wing bivalue cells and the ends of the external strong link are often weak links to which conventional coloring does not apply. I showed the "colors" within the W-Wing bivalues only to illustrate how they are "excited" by the external strong link. In other words, one of the r-g values in the bivalue cells must be false; but the other isn't necessarily true. |
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cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada
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Posted: Tue Aug 07, 2007 1:08 am Post subject: |
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Cheers Asellus: I appreciate that - though it will take a while to absorb it all. Four months ago I was still only into naked or conjugal pairs (or is conjugate pairs).
Do you think explanations like yours should be copied to the new Technique Forum?
Craig |
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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
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Posted: Tue Aug 07, 2007 5:59 am Post subject: |
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Hmmm...
Maybe they were both naked and conjugal pairs! I'm sure opinions would differ as to whether your budding mastery of sudoku is a step up or down!
As to the Technique forum, I leave that to the moderators. I believe that there is a need for a clear W-Wing posting since the term is not clearly defined elsewhere in any readily accessible form and must frequently baffle new visitors. |
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nataraj
Joined: 03 Aug 2007 Posts: 1048 Location: near Vienna, Austria
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Posted: Tue Aug 07, 2007 7:07 pm Post subject: |
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nataraj's theory of sudoku forum thread size (still lacking proof)
Conjecture: The number of posts to a thread on dailysudoku.com discussion page is directly proportional to the number of days until the next "very hard" puzzle.
---------
It's been a long 4 days ...... (sigh) |
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